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A101334
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n^n - (n+1)^(n-1).
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4
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0, 0, 1, 11, 131, 1829, 29849, 561399, 11994247, 287420489, 7642052309, 223394306387, 7123940054219, 246181194216957, 9165811757198641, 365836296342931439, 15584321022199735823, 705800730789742512401, 33866021217511735389485, 1716275655660313589123979
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OFFSET
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0,4
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COMMENTS
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b(n) = n^n mod (n+1)^(n-1) begins: 0, 0, 1, 11, 6, 533, 13042, 37111, 2428309, ...
a(n) is the number of functions f:{1,2,...,n}->{1,2,...,n} with at least one cycle of length >= 2. - Geoffrey Critzer, Jan 11 2013
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..150
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FORMULA
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E.g.f.: 1/(1-T(x)) - exp(T(x)) where T(x) is the e.g.f. for A000169. - Geoffrey Critzer, Jan 11 2013
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EXAMPLE
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a(3) = 3^3 - 4^2 = 27-16 = 11.
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MATHEMATICA
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ReplacePart[Table[n^n-(n+1)^(n-1), {n, 0, nn}], 0, 1] (* Geoffrey Critzer, Jan 11 2013 *)
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PROG
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(PARI) for(x=1, 20, print( x^x-(x+1)^(x-1) ))
(Python)
for n in range(33):
print n**n - (n+1)**(n-1),
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CROSSREFS
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Cf. A046065.
Sequence in context: A082148 A075509 A061113 * A222872 A068645 A097258
Adjacent sequences: A101331 A101332 A101333 * A101335 A101336 A101337
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KEYWORD
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nonn
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AUTHOR
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Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 24 2004
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EXTENSIONS
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a(0), Python program and b(n) in comments added by Alex Ratushnyak, Aug 06 2012
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STATUS
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approved
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